The value of `^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m` is equal to (a)`^m+n C_(n-1)` (b)`^m+n C_(n-1)` (c)`^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1)` (d)`^m+1C_(m-1)`

C_(0)-3C_(1)+5c_(3)+....+(-1)^(n)(2n+1)C_(n) is equal to

If ^(m)C_(1)=^(n)C_(2) then 2m=nb2m=n(n+1) c.2m=(n-1)d2n=m(m-1)

^(n)C_(m)+^(n-1)C_(m)+^(n-2)C_(m)+............+^(m)C_(m)

Prove that mC_(1)^(n)C_(m)-^(m)C_(2)^(2n)C_(m)+^(m)C_(3)^(3n)C_(m)-...=(-1)^(m-1)n^(m)

The value of determinant |1 1 1^m C_1^(m+1)C_1^(m+2)C_1^m C_2^(m+1)C_2^(m+2)C_2| is equal to 1 b. -1 c. 0 d. none of these

(.^(n)C_0+.^(n+1)C_1+.^(n+2)C_2+....+.^(n+m)C_m)/(.^(m)C_0+(.^(m)C_1)+(.^(m+1)C_2)+...+(.^(m+n)C_(n+1)) (A) 1 (B) 2 (C) 3 (D) 4

Using binomial theorem (without using the formula for sim nC_(r)), prove that ^nC_(4)+^(m)C_(2)-^(m)C_(1)^(n)C_(2)=^(m)C_(4)-^(m+n)C_(1)^(m)C_(3)+^(m+n)C_(2)^(m)C_(2)-^(m+n)C_(3)^(m)C_(1)+^(m+n)C_(4)

If m in N and m>=2 prove that: |111^(m)C_(1)^(m+1)C_(1)^(m+2)C_(1)^(m)C_(2)^(m+1)C_(2)^(m+2)C_(2)|=1